Before October 2008 the interest rate in US was high compared to after October the interest rate was below 1% and by November and December it was around 0.15%. If we look at the interest rate provided by US Federal Reserve, in 30th of September 2008 interest rate was 2.03 percent and 1st of October 2008 the interest rate was 1.15, if we look at the exchange rate provided by x-rates on 30th of September 2008, 1 Euro was 1.408 USD and 1 GBP was 1.7801 USD. On the 1st of October the exchange rates: 1 Euro was 1.405 USD and 1 GBP was 1.779 USD. During these two days the interest rate was not below 1 percent but there were some changes in USD. If we look at the interest rate on 2nd of October when the interest rate was 0.67 percent, 1 euro was 1.384 USD and 1 GBP was 1.764 USD. The US dollar got stronger by day in these three days, on the 3rd and 4th of October the interest rate was 1.1 percent and it increased compared to 2nd of October and 1 Euro was 1.381 and 1 GBP was 1.773 USD. We can see that USD got weaker to GBP and USD was stronger to Euro. It shows that some currencies respond towards the interest rate more efficiently compared to other currencies. Interest rate is one of the factors that can have impact on the USD but there are other factors that impacts on the exchange rate.
According to US Federal Reserve, after 2009 the interest rates were below 0.2 percent, but the exchange rates during this year was very interesting. In March 1 Euro was 1.4178 USD but starting from April and by December 1 Euro was 1.621 USD. During this year USD got so much weaker even that interest rate was stable below 0.2. It shows that the interest rate have some impact only in short period of time, but in long period the exchange rates will depend on other factors. One of the other factor that influences is the price of oil.
Another information I found interesting is the Foreign Exchange Data provided by New York Federal Reserve. They do not provide daily data, therefore it is hard to use this as an information to predict the future interest rates. In this Foreign Exchange Data they show how much of other currencies were bought and how much of USD was sold to other currencies to banks around the world. It would have been one of the best ways to know the exchange rates if the data was provided more frequently but the latest one is on 2013. It could have been predicted with Demand and Supply method.
I suggest the best way to predict the future exchange rate would be watching the news, because the politics have great influence on the exchange rate. Exchange rate does not only depend on the US economy but it also depends on the economy of other countries.